Construction and enumeration for self-dual cyclic codes of even length over [formula omitted

Abstract

Let F2m be a finite field of cardinality 2m, R=F2m+uF2m(u2=0) and s,n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length 2sn and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over F2m of length 2s+1n can be obtained from self-dual cyclic code over R of length 2sn and by a Gray map preserving orthogonality and distances from R onto F2m2.